Effects of Breathing on an Interferometer

1. Effects of Breathing on an Interferometer Susan Gosse Daniel Freno Junior Lab II

2. Breath Affects Interference Fringes • We see roughly ½ of a fringe shift when someone breaths on air in the interferometer • Theories as to why: • Different temperature results in different nair • Bernoulli pressure changes result in different index of refraction (nair) for air • Water vapor from breath changes nair • Higher CO2 content changes nair • “Stellar Aberration” effects due to wind velocity • Assumptions • Path length of 5 cm • Temperature between 21 ºC (normal) and 37 ºC • Humidity between 35% (normal) and no more than 70% • Pressure possibly lowered from 98 kPa – not much though

3. Simplified Equation with T, p, RH • p = pressure in kPa • t = temperature in Celsius • RH = relative humidity in percent (ranges from 0 to 100) • Valid ONLY for wavelength ≈ 633 nm • Agrees with full Ciddor equation within 5 x 10-5 for • 90 kPa < p < 110 kPa • 0 % < RH < 70% • 350 μmol/mol < CO2 concentration < 550 μmol/mol • Dependence approximately linear for pressure, humidity • Stronger, more complicated dependence for temperature

4. Looking at Temperature • Temperature plays HUGE role • Max expected shift is 2 fringes • 21 ºC to 37 ºC • Enough for effect seen Δm ≈ 2

5. Bernoulli on Compressible Fluids • Based on mass conservation and assumption of no heat transfer, Bernoulli’s equation says that as velocity increases, pressure decreases (with caveats) Picture from http://en.wikipedia.org/wiki/Bernoulli's_principle

6. Bernoulli’s Equation • The amount of material entering V1 equals the amount entering V2 • The energy entering V2 equals the amount leaving V1 • Assumes no heat transfer, viscous flows, etc. • Energy is sum of • kinetic energy • gravitational energy • internal energy of fluid • p dV work energy Mass Conservation: Energy Conservation: ρ = density Φ = gravitational potential energy/unit mass Є = internal energy/unit mass

7. Bernoulli’s Equation • Thus the result ‘as pressure goes down, velocity goes up’ • Assuming level height (dropping gravity term) microscopically • When velocity increases, it means that a greater proportion of each molecule’s energy is directed in the forward direction • Less energy is directed outward in other directions • Pressure is a result of this outward motion • Thus less pressure

8. Looking at Pressure • Pressure can play big role • Would need ΔP = 1 kPa to shift ½ fringe • Doubtful we are creating this much change Δm ≈ 0.5

9. Looking at Humidity • Humidity plays small role • Even if we went from 0% to 70%, only 1/10th fringe • Not responsible for effect Δm ≈ 0.1

10. CO2 Effects • The Engineering Metrology Toolbox website suggests that CO2 effects are negligible compared to other effects • Closed rooms typically have concentration of 450 μmol/mol (μmol/mol = ppm = parts per million) • 300 μmol/mol is lowest concentration likely to be found normally • 600 μmol/mol is highest likely to find in an indoor setting • Using the Ciddor calculator with standard values and varying CO2 concentrations from 300 to 600 μmol/mol • n = 1.000261742 for 300 μmol/mol • n = 1.000261783 for 600 μmol/mol • Δn = 4.1 x 10-8 • Δ fringes = 0.01 • Caveat that extreme range could exceed equation limits of validity

11. Aberration Effects • A perpendicular velocity added by the breath could cause the light to travel a longer path length • Similar to stellar aberration • Unlikely since very slow velocity compared to speed of light http://en.wikipedia.org/wiki/Aberration_of_light

12. Conclusion • Most likely, effect of ½ fringe shift is due to temperature • Can easily account for this difference and more • Pressure could be cause, but unlikely since need 1 kPa change • Would have to be further tested to determine • Humidity and CO2 are NOT the causes • Aberration is unlikely due to low velocity of breath

13. Dependence on Temp, Pressure • Where • T = temperature • p = pressure • α= 0.00366 • βT= (1.049 – 0.0157T)10-6 • β15= 0.8135X10-6

14. Dependence on Pressure

15. Pressure vs. Fringes

16. Pressure vs. Index of Refraction

17. Experimental Results for nair • Trial one : nair = 1.00021 • Trial two: nair = 1.00021 • Theory tells us that nair = 1.00026 – this small discrepancy may be due to measurement inaccuracies, or possibly to the effect of the glass plates

18. Feynman Sprinkler

19. Index of Refraction Calculator

20. Index of Refraction Calculator

21. Optical Path Length Pressure chamber n L • The length traveled by light with the index of refraction of the medium taken into account • s = 2nL • s is the optical path length, n is the index of refraction and L is the length of the vacuum chamber • Rememberthe light passes through the chamber twice (factor of 2) • ∆s = 2∆nL CHANGE in Optical Path Length • Shift of m number of fringes ∆s = 2∆nL  ∆n = ∆s/2L • If ∆s is one wavelength, then m is one fringe • ∆n = λ/2L  ∆n = mλ/2L  m = 2∆nL/ λ

22. Index of Refraction: Theory • na = index of refraction • cv = speed of light in vacuum • ca = speed of light in air • f = frequency of light • L = length of chamber • wv = no. wavelengths passing through chamber in vacuum • wa = no. wavelengths passing through chamber in air • L/wv is equal to the wavelength of the laser • wa is found by adding measured number of fringes passed to wv

23. Index of Refraction in Air • m = 2L(na-nv)/λ • m is the number of fringes that have gone past while returning to 1 atm from vacuum: m = 30.003 • L is the length of the vacuum chamber: L = 3.81 cm • nv= 1 • λ of HeNe laser: λ = 633nm We extrapolated our line to zero pressure and the number of fringes there (y-intercept) is our m. Using this equation for all 5 sets of our data, we calculated an average value for na=1.00024. According to the above equation, from the American Handbook of Physics, where P is the pressure inside the chamber and T is the temperature of the room, na=1.00028.